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Project 2: Knight and Knave Logic Problems "Knight" and "Knave" logic puzzles were invented (or perhaps popularized) by mathematician and philosopher Raymond Smullyan. These puzzles are all set on a fictional island whose inhabitants are either knights (who always tell the truth) or knaves (who always lie "Solving" a puzzle means correctly identifying the identity of each of the inhabitants involved using logic and a set of statements made by the inhabitants. Note that it is possible to invent problems that have no solution or that have more than one possible solution. Some versions of these puzzles add a third type of inhabitant called a Spy who are allowed to make both true and false statements (we may add some spies in later). In this project, we will look at several puzzles of this type You will be expected to both solve and justify your answers using sound logical reasoning. Example: Suppose there are two inhabitants: Person A and Person B. A says: "We are both knaves". B says nothing. Solution: A cannot be a knight, as a knight could not truthfully say that they are a knave. Then A must be a knave. Since A is a knave, their statement must be a lie (that is, is has to be false). In order for that to happen, B must not be a knave, so B must be a knight 1. (1 point each) Either find the identity of each individual (knight or knave), or explain where there is more than one possible solution or no possible solution. Fully justify your solution (a) A says: "B is a knave." B says: We are both knights." (b) A says: "Either B is a knight or I am a knight. B says: "A is a knave. (c) A says: "We are either both knights or both knaves." B says: "A would tell you that I am a knave. (d) A says: "I am a knight or B is a knave." B says: "A is a knight and C is a knave." C says: "B and I are different types. (e) A says: C is a knight." B says: "A and C are both knights." C says: "A is a knight or B is a knave. (f) A says: an I are both knights or both knaes. B says: "C and I are both knights." C says: I coukd claim that A is a knave." 2 (1 point each) Suppose that we know that we have e individual of each type (knight knave, or spy). Either find the identity of each individual, or explain where there is more than one possible solution or no possible solution. Fully justify your solution (a) A says: C is a knave." B says: "A is a knight." C says: "I am the spy. (b) A says: "I am not a spy." B says: "I am not a spy. C says: "I am not a spy. (c) A says: I am a knight." B says: "I am not a spy" C says: "A is a spy." (d) A says: C is a spy." B says: "C is not a knave. C says: "If you asked me, I would say that B is the spy." 3. Invent your own puzzle involving at least 3 individuals and at least two identity types. Then, provide full solution to your puzzle. Project 2: Knight and Knave Logic Problems "Knight" and "Knave" logic puzzles were invented (or perhaps popularized) by mathematician and philosopher Raymond Smullyan. These puzzles are all set on a fictional island whose inhabitants are either knights (who always tell the truth) or knaves (who always lie "Solving" a puzzle means correctly identifying the identity of each of the inhabitants involved using logic and a set of statements made by the inhabitants. Note that it is possible to invent problems that have no solution or that have more than one possible solution. Some versions of these puzzles add a third type of inhabitant called a Spy who are allowed to make both true and false statements (we may add some spies in later). In this project, we will look at several puzzles of this type You will be expected to both solve and justify your answers using sound logical reasoning. Example: Suppose there are two inhabitants: Person A and Person B. A says: "We are both knaves". B says nothing. Solution: A cannot be a knight, as a knight could not truthfully say that they are a knave. Then A must be a knave. Since A is a knave, their statement must be a lie (that is, is has to be false). In order for that to happen, B must not be a knave, so B must be a knight 1. (1 point each) Either find the identity of each individual (knight or knave), or explain where there is more than one possible solution or no possible solution. Fully justify your solution (a) A says: "B is a knave." B says: We are both knights." (b) A says: "Either B is a knight or I am a knight. B says: "A is a knave. (c) A says: "We are either both knights or both knaves." B says: "A would tell you that I am a knave. (d) A says: "I am a knight or B is a knave." B says: "A is a knight and C is a knave." C says: "B and I are different types. (e) A says: C is a knight." B says: "A and C are both knights." C says: "A is a knight or B is a knave. (f) A says: an I are both knights or both knaes. B says: "C and I are both knights." C says: I coukd claim that A is a knave." 2 (1 point each) Suppose that we know that we have e individual of each type (knight knave, or spy). Either find the identity of each individual, or explain where there is more than one possible solution or no possible solution. Fully justify your solution (a) A says: C is a knave." B says: "A is a knight." C says: "I am the spy. (b) A says: "I am not a spy." B says: "I am not a spy. C says: "I am not a spy. (c) A says: I am a knight." B says: "I am not a spy" C says: "A is a spy." (d) A says: C is a spy." B says: "C is not a knave. C says: "If you asked me, I would say that B is the spy." 3. Invent your own puzzle involving at least 3 individuals and at least two identity types. Then, provide full solution to your puzzle
